id	author	title	date	pages	extension	mime	words	sentence	flesch	summary	cache	txt
ejde-240	Antontsev, Antontsev; Ferreira, Jorge; Piskin, Erhan	Existence and blow up of solutions for a strongly damped Petrovsky equation with variable-exponent nonlinearities	2021	18	.pdf	application/pdf	6658	376	82	= ∫ Ω |u|q(·)dx (5.6) for any u ∈ H2 0 (Ω) and 2 ≤ s ≤ q−. Where C > 1 a positive constant and H(t) = −E(t). = (1− σ)H−σ(t)H ′(t) + ε ∫ Ω (u2 t + uutt)dx+ ε ∫ Ω ∇u∇ut dx = (1− σ)H−σ(t)H ′(t) + ε‖ut‖2 − ε‖∆u‖2 + ε ∫ Ω |u|q(·)dx− ε ∫ Ω uut|ut|p(·)−2dx. (5.13) By using the definition of the H(t), it follows that −εq−(1− ξ)H(t) = εq−(1− ξ) 2 ‖ut‖2 + εq−(1− ξ) 2 ‖∆u‖2 − εq−(1− ξ) ∫ Ω 1 q(x) |u|q(·)dx, (5.14) where 0 < ξ < 1.	cache/ejde-240.pdf	txt/ejde-240.txt